Above we have a parabola with its vertex and axis of symmetry labeled.
|Equation of a Parabola|
The standard form of an equation of a parabola with
vertex (h, k)
Axis of Symmetry x = h
is written as:
If a > 0, then k is the minimum, and the parabola opens upward.
If a < 0, then k is the maximum, and the parabola opens downward.
Below, two parabolas are graphed:
Each parabola has a focus, and a directrix.
For any given point, the distance to the focus is equal to the distance to the directrix.
The Latus Rectum specifies the width of the parabola:
The smaller a is, the wider the parabola is.